Image Processing and Image Analysis for Medical
Visualization
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Classification
• Preprocessing
• Segmentation procedures
• Semi-automatic procedures
• Automatic procedures
• Applications: Segmentation of organs, lesions and vessels
• Postprocessing with morphologic operators
• Skeletization
• Quantitative analysis of medical image data
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Introduction
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Preprocessing
• Application of local or global image processing
filters that support the subsequent processing
• Examples:
• noise reduction
• edge enhancement
• contrast enhancement
• reduction of MR inhomogeneities
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Preprocessing: Definitions
• Histogram: Function that indicates the frequency of each
grey value.
• h(g) = |{p є (MN) with f(p) = g}|,
∑h(g) = M * N
• Tri-modal histogram (histogram with three distinctive
maxima)
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Preprocessing: Definitions
• Point-oriented operations
• The values of a voxel are changed (isolated), e.g.
thresholding, subtraction, lookup table
• Local filters (mask, cores)
• The values of a voxel are changed dependent on the
values in the neighborhood.
• static and dynamic filters
• Problem: treatment of edges
• Global operations
• Histogram equalization
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Noise Reduction
Overview over the filters:
• Average filter
• Linear noise filter, which flattens edges
• Median filter
• Edge-preserving noise filter, non-linear, rank filter
• Gaussian filter
• Non-linear noise filter, which flattens edges
• Sigma filter
• Non-linear noise filter
The filters (except Median) are normalized such that the sum of
the absolute values is 1.
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Noise Reduction: Median Filtering
• Procedure: The sequence of the grey values is identified in a
local surrounding (3x3, 5x5).
• Each grey value is replaced by the value which appears in the
middle during the sorting
• Example: 3x3 size, value 17, surrounding:
(8,12, 12, 17, 19, 19, 21, 22, 24): replace 17 by 19
• Similar filters: Minimum/maximum filter (after sorting the
current pixel is replaced by the minimum/maximum value →
enlargement of details)
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Noise Reduction: Median Filtering
Application of a 5x5 Median filter to an axial slice of CT data
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Noise Reduction: Median Filtering
Characteristics:
• Good suppression of pulsed noise (outliers)
• The average grey value of the image may vary
• Edge transitions are preserved
• Thin lines are suppressed
Suppression of thin lines is avoidable through a special
kernel form.
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Noise Reduction: Gaussian Filter
• Filtering with a discretized Gaussian function (Gaussian bell
curve, weighted mean value)
• Values correspond to binomial coefficients
1
1 2 1
1/16 *
2 4 2
1 2 1
1/256 *
4
6
4 1
4
16 24 16 4
6
24 36 24 6
4
16 24 16 4
1
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4 1
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Noise Reduction: Gaussian Filter
Characteristics:
• Noise in a small surrounding is suppressed.
• Sharp edges are smoothed.
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Noise Reduction: Gaussian Filter
Gaussian filter for an MRI data set; screenshots: Vtk
Reference: Schroeder et al. (1998)
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Noise Reduction: Gaussian Filter
3D ultrasound. Left: unfiltered, middle, right: moderate and strong
Gaussian filter, respectively. (Sakas, 1995)
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Noise Feduction: Model Assumptions
• Gaussian filtering assumes a normally distributed noise
• CT and X-ray images: assumption holds true
• MRI data: asymmetric Rician distribution
CT data; Gaussian mixture model, Rician distribution (Source:
Hennemuth, 2012)
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Noise Reduction: Sigma Filter
Idea: Limit the noise filtering to pixels (voxels) that do not
deviate too strong from the average value. Use of a
parameter sigma, which doesn not concretize “too
strong”.
• Calculation of the standard deviationstd_dev within a
kernel.
For each pixel (voxel) with p in the kernel with
p(i) in [-sigma *std_dev, sigma *std_dev]
calculate the average value avg
For each pixel (voxel) with p in the kernel with
p(i) in [-sigma *std_dev, sigma *std_dev]
p(i)  avg.
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Noise Reduction: Sigma Filter
Left: original CT layer, right: Sigma filtered (11x11, sigma = 1.0)
(Screenshot: MeVis ILab4, data set: Uni Essen)
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Noise Reduction: Sigma Filter
Left: original CT layer, right: Sigma filtered (11x11, sigma = 1.0)
(Screenshot: MeVis ILab4, data set: Uni Essen)
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Noise Reduction: Diffusion Filtering
• Diffusion filtering yields better results (edge-preserving
anisotropic filtering)
Reference: Lamecker at al. (2002)
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Noise Reduction: Diffusion Filtering
• Parameters primarily adjust a trade-off between accuracy (small
step size, high number of iterations) and speed
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Noise Reduction: Diffusion Filtering
Median 5x5
Diffusion filter
Original
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Noise Reduction: Summary
• Optimum quality (feature preservation and reduction of noise) is
achieved with expensive diffusion filters (numerical solution of a
set of partial differential equations)
• Simple filters, such as Gaussian, have a higher performance.
• Suitability of a filter depends on the characteristics of the noise
(probability density function)
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Reduction of MR Inhomogeneities
• Fields of the coils
inhomogeneous
• Consequence: brightening
at edges; other form of
inhomogeneity: streak
artifacts
• Correction: via modeling
(bias field)
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Reduction of MR Inhomogeneities
Correction of inhomogeneities with N3 algorithm (Sled, 1998).
Screenshot: A. Schenk, MeVis
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Preprocessing: Contrast Enhancement
• Goal: higher contrasts at object edges
• Idea: Difference between the image and the Laplace-filtered
image (Screenshots: vtk)
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Preprocessing: Sharpen
Characteristics:
• Sum of all entries: 1
• Contrast enhancement through negative values for
surrounding pixels
• Examples: Sharpness factor 0.5, radius 1 and 1.5, resp.
0
-0.5
0
-0.5 0
3
-0.5
-0.5 0
-0.5 -0.5 -0.5
-0.5
5
-0.5
-0.5 -0.5 -0.5
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Preprocessing: Sharpen
Application of a Sharpen filter with 11x11 kernel
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Preprocessing: Sharpen
Unsharp masking:
• Idea: The strongly smoothed original image (generated
e.g. through Gaussian filtering) is digitally subtracted from
the original image. Thus, the unsharp areas are faded out
(masked).
5x5 Gaussian filter, CT data set Uni Essen
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Preprocessing: Problems
• Contrast enhancement is combined with noise
enhancement.
• Noise reduction also decreases contrasts.
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Preprocessing: Adaptive Neighborhoods
• Problems during preprocessing are related to the fixed kernel
sizes. In some image parts, they are too small, in others they are
too large.
• Idea: Adaptive neighborhoods, which adapt in size and form to
local image characteristics (grey values, gradients, textures, …).
• Procedure: Starting from each central pixel/voxel, pixels/voxels in
the neighborhood, which are “similar” in relation to the chosen
image characteristics, are searched.
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Preprocessing: Adaptive Neighborhoods
• Similarity is defined through an additive or multiplicative
tolerance criterion. (i,j) is the central pixel/voxel. “f” are,
e.g., grey values. “T1, T2” are threshold values.
• Additive:
|f(k,l) – f(i,j)|  T1
• Multiplicative:
(|f(k,l) – f(i,j)| )/ f(i,j)  T2
Specific procedure:
Search for pixels/voxels in the direct neighborhood that
fulfill the similarity criterion.
Search for all of these pixels/voxels in their neighborhood
(recursive).
Criterion for cancellation: no further pixels/voxels fulfill the
criterion.
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Preprocessing: Adaptive Neighborhoods
Applications:
• Noise suppression (Gaussian, Median)
• Edges are better preserved.
• Tolerance criterion depends on the type of noise.
• Unsuitable in case of pulsed noise.
• Histogram modification
• Instead of global equalization: application in adaptive
neighborhood.
• Application in case of image inhomogeneities, e.g. MR data.
• Contrast enhancement
• Medium contrasts may be specifically enhanced through the
use of adaptive neighborhoods. (Strong contrasts need no
enhancement, weak contrasts can mostly be traced back to
noise.)
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Preprocessing: Highlighting of Elongated Structures
Elongated structures are identified via an Eigenvalue
analysis of the Hessian matrix (approximated 2nd
derivatives).
Major application: vasc. Structures -> vesselness filtering
More about this topic: In the exercises!
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